with initial conditions
\(u(0) = 0, [D^{\alpha-n+1}u(x)]_{x=0} = b_{n-1} \geq 0,[D^{\alpha-n+j}u(x)]_{x=0} = b_{n-j}, b_{n-j} \geq \sum^{j-1}_{k=1}a_{k}b_{k+n-j}, j = 2,3,\ldots,n-1,n-1\leq\alpha\leq n,n\in\i\) where
\(\user1{L}(D)=D^{\alpha}-\sum^{n-1}_{j=1}a_jD^{\alpha-j},a_j>0,\forall j,D^{\alpha-j}\) is the standard Riemann–Liouville fractional derivative. Further the conditions on aj’s and f, under which the solution is (i) unique and (ii) unique and positive as well, are given